Isothermal autocatalytic reaction

The CSTR is, in many ways, the easier to set up and operate, and to analyse theoretically. Figure 6.1 shows a typical CSTR, appropriate for solution-phase reactions. In the next three chapters we will look at the wide range of behaviour which chemical systems can show when operated in this type of reactor. In this chapter we concentrate on stationary-state aspects of isothermal autocatalytic reactions similar to those introduced in chapter 2. In chapter 7, we turn to non-isothermal systems similar to the model of chapter 4. There we also draw on a mathematical technique known as singularity theory to explain the many similarities (and some differences) between chemical autocatalysis and thermal feedback. Non-stationary aspects such as oscillations appear in chapter 8. 

Gray, P. and Scott, S. K. (1985). Sustained oscillations and other exotic patterns of behavior in isothermal reactions. J. Phys. Chem., 89, 22-32. Lin, K. F. (1981). Multiplicity, stability and dynamics for isothermal autocatalytic reactions in CSTR. Chem. Eng. Sci., 36, 1447-52. 

Scott, S. K. (1987). Isolas, mushrooms and oscillations in isothermal, autocatalytic reaction-diffusion equations. Chem. Eng. Sci., 42, 307-15. 

Gray, B. F., Scott, S. K. and Gray, P., 1984, Multiplicity for isothermal autocatalytic reactions in open systems the influence of reversibility and detailed balance. J. Chem. Soc. Faraday Trans. 1 80, 3409. 

A similar analysis of reactions with autocatalysis by the final products [equations (15) and (16), see Figs. 2 and 3] is significantly simpler and we leave it for the reader. A simpler, but also weaker algebraic (rather than exponential, in accordance with Arrhenius law) dependence of the reaction rate on the concentration in an isothermic autocatalytic reaction causes much less complete combustion at the limit of extinction. 

B.1.11 In a study of isothermal autocatalytic reactions. Gray and Scott (1985) considered a hypothetical reaction whose kinetics are given in dimensionless form by... 

Enhancement of non isothermal autocatalytic reactions by intraparticle diffusion... 

The general rule is that combinations of isothermal reactors provide intermediate levels of performance compared with single reactors that have the same total volume and flow rate. The second general rule is that a single, piston flow reactor will give higher conversion and better selectivity than a CSTR. Autocatalytic reactions provide the exception to both these statements. 

DSC can be used effectively in the isothermal mode as well. In this case, the container with the sample is inserted into the DSC preheated to the desired test temperature. This type of experiment should be performed to examine systems for induction periods that occur with autocatalytic reactions and with inhibitor depletion reactions. (Reactions with induction periods can give misleading results in the DSC operated with increasing temperature scans.) Autocatalytic reactions are those whose rates are proportional to the concentration of one or more of the reaction products. Some hydroperoxides and peroxy esters exhibit autocatalytic decomposition. Inhibitor depletion can be a serious problem with certain vinyl monomers, such as styrene and acrylic acid, that can initiate polymerization at ambient temperatures and then selfheat into runaways. Isothermal DSC tests can be used to determine a time to runaway that is related to the inhibitor concentration. 

Fig. 3.8. Representation of the onset, growth, and death of oscillations in the isothermal autocatalytic model as /z varies for reaction with the uncatalysed step included, showing emergence of the stable limit cycle at and its disappearance at n. ...

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

P. Gray and S. K. Scott. Autocatalytic reactions in the isothermal continuous stirred tank reactor Isolas and other forms of multiplicity. Chem. Eng. ScL 38, 29-43 (1983) Autocatalytic reactions in the isothermal continuous stirred tank reactor Oscillations and instabilities in the system A + 2B —> 3B, B —> C. Chem Eng. ScL 34, 1087-1097 (1984). 

The literature on this model reaction is already vast and a complete bibliography would be of great use to the mathematical modeler. Of particular interest are A. d Anna, P. G. Lignola, and S. K. Scott. The application of singularity theory to isothermal autocatalytic open systems The elementary scheme A + mB = (m + 1) B. Proc. Roy. Soc. Lond. A 403, 341-363 (1986) and S. R. Kay, S. K. Scott, and P. G. Lignola. The application of singularity theory to isothermal autocatalytic open systems The influence of uncatalyzed reactions. Proc. Roy. Soc. Lond A 409, 433-448 (1987). 

Gray, P. and Scott, S. K., 1984, Autocatalytic reactions in the isothermal continuous stirred tank reactor. Chem. Engng ScL 39,1087-1097. 

Figu re 12.1 Comparison of autocatalytic (a) an nth-order (ri) reactions in an isothermal DSC experiment performed at 200°C. Both reactions present a maximum heat release rate of lOOWkg 1 at 200°C. The induction time of the autocatalytic reaction leads to a delay in the reaction course. 

This is due to the fact that under isothermal conditions, the nth-order reaction presents its maximum heat release rate at the beginning of the exposure to initial temperature, whereas the autocatalytic reaction presents no heat release rate at this time. Thus, temperature increase is delayed and only detected later after an induction period, as the reaction rate becomes sufficiently fast. Hence acceleration, due to both product concentration and temperature increase, becomes very sharp. 

Figu re 12.4 Comparison of a strongly autocatalytic reaction with a weak autocatalytic reaction (dashed line). Isothermal DSC experiment at 200°C. The heat release rate for the strong autocatalytic reaction is zero at the beginning of the exposure. 

Thanks to its versatility, this model has proved to describe a great number of autocatalytic reaction systems [5]. Systems with a slow initiation reaction are called strong autocatalytic. Because the rate of the initiation reaction is low, product is formed slowly, leading to a long induction time under isothermal conditions. For such systems, the initial heat release rate is low or practically zero. Consequently, the reaction may remain undetected for a relatively long period of time (Figure 12.4). When the reaction accelerates, such an acceleration appears suddenly and may lead to runaway. A strong autocatalytic reaction is formally equivalent to a Prout-Tompkins mechanism. 

This method was validated with over 100 substances and compared with the results of the classical study by isothermal experiments. For apparent activation energies above a level of 220 kj mol"1, 100% of the samples showed an autocatalytic character in isothermal experiments. This method can be used as a screen to distinguish clearly autocatalytic reactions from others that should be studied by isothermal experiments. This reduces the number of isothermal experiments required. 

To obtain a more realistic estimation of the behavior of an autocatalytic reaction under adiabatic conditions, it is possible to identify the kinetic parameters of the Benito-Perez model from a set of isothermal DSC measurements. In the example shown in Figure 12.11, the effect of neglecting the induction time assumes a zero-order reaction leading to a factor of over 15 during the time to explosion. Since this factor strongly depends on the initial conversion or concentration of catalyst initially present in the reaction mass, this method must be applied with extreme care. The sample must be truly representative of the substance used at industrial scale. For this reason, the method should be only be applied by specialists. 

What do you think about the statement For a strongly autocatalytic reaction, the isothermal induction time is close to TMRld ... 

---